Step 1: Materials and tools
When you go to the store to buy a replacement stopper, you want to look for a pop-up assembly. Most are 1 1/4 x 12 inches. They come with a lift rod and linkage. Often you can buy the linkage rod with ball and a stopper without buying the whole pop-up assembly. I chose to replace the whole pop-up assembly. The cost is very little more and I am beginning with all new parts.
A slip joint pliers is a good tool to have nearby. An adjustable wrench and a screwdriver may be needed, but it happened that I did not use them on this project. A sealant of some type will also be required. Shown is a container of plumber's putty. As I was in the middle of replacing the pop-up assembly I discovered that my plumber's putty has a warning label that says it is not to be used with marble or plastic. I ran to a store to get some silicone sealant formulated for use in the bathroom, including with plastics.